Saturday, April 26, 2003

One of the things that occasionally puzzles me is why movie theatres don't use Ramsey pricing, whereby a producer of multiple goods apportions the fixed and common costs to the final product prices in inverse proportion to the price elasticity of demand.

OK, I'd better step back a bit and explain. Many industries incur fixed and/or common costs. If you consider local phone service and long distance service to be two different products, then the costs of running copper wire to your house is a fixed cost (in that it is incurred whether or not you sign up for service) and a common cost (in that you can't trace it specifically to local phone service or long distance).

So the problem in such instances is how to incorporate those costs into the final product prices. A guy named Frank Ramsey came up with a theory on how to do this (actually his theory applied specifically to taxation, but was later extended to this case by Boiteux). His theory was that when you look at the demand for the various products at issue (without the fixed and/or common costs apportioned), you should try to figure out how to add those costs into the prices without changing the proportional demand for each product.

To do this, you have to allocate common costs in proportion to the inelasticity of demand for each individual product. Thus, if one product has a high inelasticity of demand (as is the case with food, cigarettes, etc.), more common costs should be incorporated into that product's price. And vice versa -- products for which the demand is elastic should pay for fewer common costs. Thus, second-best allocative efficiency is achieved.

What does this have to do with movie theatres? Well, they have a lot of fixed and common costs -- the costs of paying ticket sellers and ushers; the costs of running a very large building, etc. Yet they charge the same price for each movie -- The Matrix Reloaded costs the same $8.00 as The Real Cancun. There's no reason it should be this way. Given that theatres have to recover a certain amount of common costs, it would make more sense for them to raise the prices of movies that are immensely popular (as to which the demand is sure to be more inelastic) and lower the prices of movies that are duds (as to which the demand is more elastic).

So why don't they do this? I don't know. It's just one of the things that puzzles me from time to time.

While I'm at it, I might as well sing a few praises of Frank Ramsey. I first came across him when I read his 1927 article on "Facts and Propositions," where he laid out the redundancy theory of truth (similar to Quine's disquotational theory). Later, when I had occasion to read several books on natural monopoly regulation, I came across the concept of Ramsey pricing. Little did I imagine that it was the same Ramsey.

A Google search, however, revealed that yes, indeed, it was the same Frank Ramsey. And these were not his only accomplishments. He also wrote several other important works of philosophy, mathematics and probability theory, translated Wittgenstein's Tractatus and served as Wittgenstein's thesis advisor at Cambridge, wrote another economics paper that Keynes later called "one of the most remarkable contributions to mathematical economics ever made," and had as a teenager learned to read German in about 10 days. If you want to read more about Ramsey's remarkable life and career, this page is probably the best resource. Ramsey, more than just about anyone else I can think of, reminds me of the polymathic achievements of John von Neumann, whose work on game theory was (wouldn't you know it) foreshadowed by one of Ramsey's papers on utility theory. And to think -- Ramsey became ill and died at the age of 26! (If only he had lived a full life . . . .)